A Concise Introduction to Analysis

Daniel W. Stroock

ISBN 10: 3319244671 / ISBN 13: 9783319244679

Edité par Springer International Publishing, 2015

A Concise Introduction to Analysis | Daniel W. Stroock | Taschenbuch | xii | Englisch | 2015 | Springer International Publishing | EAN 9783319244679 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand. N° de réf. du vendeur 104281206

Synopsis :

This book provides an introduction to the basic ideas and tools used in mathematical analysis. It is a hybrid cross between an advanced calculus and a more advanced analysis text and covers topics in both real and complex variables. Considerable space is given to developing Riemann integration theory in higher dimensions, including a rigorous treatment of Fubini's theorem, polar coordinates and the divergence theorem. These are used in the final chapter to derive Cauchy's formula, which is then applied to prove some of the basic properties of analytic functions.
Among the unusual features of this book is the treatment of analytic function theory as an application of ideas and results in real analysis. For instance, Cauchy's integral formula for analytic functions is derived as an application of the divergence theorem. The last section of each chapter is devoted to exercises that should be viewed as an integral part of the text.
A Concise Introduction to Analysis should appeal to upper level undergraduate mathematics students, graduate students in fields where mathematics is used, as well as to those wishing to supplement their mathematical education on their own. Wherever possible, an attempt has been made to give interesting examples that demonstrate how the ideas are used and why it is important to have a rigorous grasp of them.

À propos de l?auteur: Before he retired, Stroock had been on the faculty of several universities, most recently M.I.T. The majority of his work has to do with analytic aspects of probability theory, especially the application of probability theory to partial differential equations. He is a member of the American Mathematical Society, the American Academy of Arts and Sciences, the National Academy of Sciences, and the Polish Academy of Arts and Sciences.

Détails bibliographiques

Titre : A Concise Introduction to Analysis
Éditeur : Springer International Publishing
Date d'édition : 2015
Reliure : Taschenbuch
Etat : Neu